In this paper a method is presented for solving the equilibrium problem with axisymmetry for arbitraryly given plasma configurations. First, the boundary value problem of equilibrium equation is solved by finite element method for a given plasma boundary and current distribution. Then, based on virtual-casing principle, the virtual-casing current which produces the maintaining magnetic field requisite for the equilibrium is obtained by using solution of the equilibrium equation. The field of virtual-casing current, i.e. the maintaining field inside plasma is calculated. The current distribution of maintaining field on a certain contour outside the plasma is found by means of solving the integral equation. The main difficulty confronted in solving the integral equation problem is that one has to deal with an incorrectly posed problem. We have solved the incorrectly posed Fredholm integral equation of first kind, using a method of singular value decomposition. This method is simple and effective in solving such an equilibrium problem.We have considered seven types of plasma configuration including circular, elliptic, doublet, race-track, D-, back D- and banana shapes and three kinds of plasma current distribution including quasi-uniform, diffusion-type and skin-type distribution. Three type of current distribution for maintaining field are obtained in a given circular-, elliptic- and -shapes. For the models as mentioned above, the current distribution of maintaining field and the field itself are given. The total currents of maintaining field and total plasma currents are compared with each other. Some influences of the maintaining fields on stability is discussed.